2. Integrate: a) Sx cos(x²) dx g) [3 cos(2nx) dx b) S tan³ x sec²x dx h) Se2% sin(e²*) dx c) S cot x dx d) S sin’ x cos x dx e) S tan² x dx (use a Pythagorean Id.) f) S(x – 1) cos(x² – 2x) dx

Q: Integrate S(cos x)e*+sin xdx B. et-sinx + C A. -e4+sin x + C c. e4+sinx + C D. e-4+sinx +C A В C D

A: Given: I=∫cosxe4+sinxdx  ....(1)   We know that; ∫eax+bdx=1aeax+b+C

Q: s+2s ds s2+1

A: I have stated the used formulas in the solution.

Q: Determine 1 dx , 4x2 +1 (i) (ii) x cos x dx .

A: Determine.  (i).  ∫14x2+1dx             ⇒∫14x2+1dx=14∫1x2+14dx  ⇒∫14x2+1dx=14∫1x2+122dx…

Q: Let f(x) = (8 sin a + 4 cos a)tan %3D f'(x) = %3D

A: We will differentiate the given function using the product rule of differentiation

Q: Evaluate Se²x 2x Se²x 2x cos (5x) dx. cos (5x) dx = e2x. (5 sin (5x) + 2 cos (5x)) 19 + C

A:

Q: | (cos c+ 1) dc;let x be constant

A:

Q: V. Show that: 1. [(cosx-sin x)'dx = x+ cos 2x +C 2.

A:

Q: cos 2x 12) S 2cos2x sin x – sin x dx -

A: To integrate:∫cos2x2cos2xsinx-sinxdx Solution: ∫cos2x2cos2xsinx-sinxdx On simplifying further we…

Q: (h) (1 – cos² r) (1+ cot? r) = 1 %3D

A: you can clearly understand if you follow the below solution

Q: a dx = 1+ sin(ax) Select one: a. tan(ax) – sec(az) + C b. ax + In | csc(az) – cot(az)| + C c. In |1+…

A:

Q: Function dy du dy du dx dx = (5x³ – 7x² + 2x – 3)*) _y = csc(x² – 3) y = 5x² – . y = V5x2 – 4 _y =…

A:

Q: Pls help ASAP

A: To find - If sinθ = -0.6 and secθ < 0, then tanθ is ?

Q: Set u = sec (8x) + tan(8 - x). • Step 1: ● ● ● du dx Step 2: = dx = Step 3: 8( sec (8x tan (8x)) +…

A: We need to find the given integral:       ∫sec28x+sec8x·tan8xsec8x+tan8x dx

Q: -1 Let f(x) = (3 sin z + 4 cos z)tan f'(x) = %3D

A: Given  f(x)=(3sinx+4cosx)tan-1xTo find f'(x):

Q: b) if J(zf64)} - 39ga) ) ce = Sin () %3D and S(3f (x)+9 6)) dx = tan () 2. 2. +596)) dx

A:

Q: Evaluate: 4S d sin(t?)dt dx x 3x²sin(x“) – sin(x²) b. 2x°cos(x°) – 2xcos(x²) a. 3x²cos(x^) – cos(x²)…

A:

Q: Differentiate y= cos y2x +1 sin 2x+1 A. V2x+1 sin 2x+1 B. V2x+1 sin 2x+1 C. V2x-1 sin 2x-1 D. V2x+1

A: Please refer the attached image for complete solution. THANK YOU.

Q: 2. Integrate | sin x cos? x dx

A:

Q: ,2 Compute x² cos(x³ + 3) dx

A:

Q: 2- Calculate y": y = 5x2 Sin (3z) - 2x Cos (5x)

A:

Q: (d) ſ tan² 3t dt 5 cos? x – 3 tan x dx - (e) S cOs X

A: The integration of the integrals is d) tan2(3t)  e) (5cos2x-3tanx) /cosx

Q: (d) ƒ COS √1+sin x dx, (e) cos(lnx) S dx Т

A:

Q: 13. Evaluate: sin(x²) dx A) 2x cos(x2) B) 2x sin(x?) C) 2x cos 2x D)2x cos x 14. Find the derivative…

A: To find Evaluate the integral: